Monday, May 24

Nonlinear Dynamics of Partial Differential Evolution Equations and Applications

10:00 AM-12:00 PM
Room: Wasatch A/B

In the past decade, a great deal of progress was made in using dynamical systems and solitons to studying the dynamics of nonlinear partial differential equations. Many applications, such as nonlinear optics, furnish examples that exhibit both very regular and chaotic dynamics. There has, therefore, always existed a beneficial mutual interaction between these fields and various branches of dynamical systems, including, more recently, those pertaining to partial differential equations. The speakers in this minisymposium will illustrate this interaction by describing the dynamical behavior of specific partial differential equations that arise in nonlinear optics and other applied fields, and discussing several new techniques. These include dynamical systems analysis of homoclinic orbits and chaotic dynamics in partial differential equations, turbulence theory, kinetic equations, numerical computations and diagnostics for nonlinear partial differential equations, and perturbation theory for near-integrable partial differential equations and solitons. Applications will include semiconductor lasers, long ring-cavity gas lasers, and fiber optics. Analytical and numerical studies will be presented.

Organizers: Gregor Kovacic
Rensselaer Polytechnic Institute

10:00-10:25 Soliton Perturbations and the Random Kepler Problem
Jared C. Bronski, University of Illinois, Urbana-Champaign; Fatkhulla Kh. Abdullaev, Physical-Technical Institute, Uzbekistan; and NewG. Papanicolaou, Stanford University
10:30-10:55 Shilnikov Manifolds in Coupled Nonlinear Schrödinger Equations
George Haller, Brown University
11:00-11:25 Weak Turbulence with Applications to Semiconductor Lasers and Fiber Optics
Yuri Lvov, Los Alamos National Laboratory
11:30-11:55 Dynamics of Long Ring Lasers
Gregor Kovacic, Organizer; and Ilya Timofeyev, Courant Institute of Mathematical Sciences, New York University

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MMD, 4/11/99
LMH, 1/8/99; tjf, 2/2/99